• Medientyp: E-Artikel
  • Titel: A Generalized Coupon Collector Problem
  • Beteiligte: Xu, Weiyu; Tang, A. Kevin
  • Erschienen: Cambridge University Press (CUP), 2011
  • Erschienen in: Journal of Applied Probability
  • Sprache: Englisch
  • DOI: 10.1017/s0021900200008639
  • ISSN: 0021-9002; 1475-6072
  • Schlagwörter: Statistics, Probability and Uncertainty ; General Mathematics ; Statistics and Probability
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  • Beschreibung: <jats:p>This paper presents an analysis of a generalized version of the coupon collector problem, in which the collector receives <jats:italic>d</jats:italic> coupons each run and chooses the least-collected coupon so far. In the asymptotic case when the number of coupons <jats:italic>n</jats:italic> goes to infinity, we show that, on average, (<jats:italic>n</jats:italic>log<jats:italic>n</jats:italic>) / <jats:italic>d</jats:italic> + (<jats:italic>n</jats:italic> / <jats:italic>d</jats:italic>)(<jats:italic>m</jats:italic> − 1)log log<jats:italic>n</jats:italic> + <jats:italic>O</jats:italic>(<jats:italic>mn</jats:italic>) runs are needed to collect <jats:italic>m</jats:italic> sets of coupons. An exact algorithm is also developed for any finite case to compute the exact mean number of runs. Numerical examples are provided to verify our theoretical predictions.</jats:p>